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06 Apr 2022, 02:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
41% (01:57) correct
59%
(01:53)
wrong
based on 218
sessions
History
Date
Time
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Not Attempted Yet
The average (arithmetic mean) of a list of six numbers is equal to 0. What is the positive difference between the number of positive numbers in the list and the number of negative numbers in the list?
(1) Each of the positive numbers in the list equals 10.
(2) Each of the negative numbers in the list equals −5.
Are You Up For the Challenge: 700 Level Questions
(1) Each of the positive numbers in the list equals 10.
(2) Each of the negative numbers in the list equals −5.
Are You Up For the Challenge: 700 Level Questions
06 Apr 2022, 08:13
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Step 1: Analyse Question Stem
The average of a list of six numbers is equal to zero. Therefore, the sum of these numbers is zero. It is important to consider different cases that ensure that the sum of the numbers is zero.
We need to find the positive difference between two numbers – the number of positive numbers in the list and the number of negative numbers in the list.
The term positive difference may hint that the two numbers are distinct and not the same.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: Each of the positive numbers in the list equals 10.
Case 1: The six numbers could be 10, 10, -10, -5, -5 and 0. There are two positive numbers here and three negative numbers; the positive difference between the two types of numbers is 1.
Case 2: The six numbers could be 10, -2, -2, -2, -2, and -2. There is one positive number and five negative numbers; the positive difference between the two types of numbers is 4.
These are two different answers to the question asked.
Statement 1 is insufficient, answer options A and D can be eliminated.
Statement 2: Each of the negative numbers in the list equals −5.
Case 1: The six numbers could be -5, 1, 1, 1, 1 and 1. There are five positive numbers here and one negative number; the positive difference between the two types of numbers is 4.
Case 2: The six numbers could be -5, -5, 10, 0, 0 and 0. There is one positive number and two negative numbers; the positive difference between the two types of numbers is 1.
These are two different answers to the question asked.
Statement 2 is insufficient, answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: Each of the positive numbers in the list equals 10.
From statement 2: Each of the negative numbers in the list equals -5.
Case 1: The six numbers could be 10, 10, -5, -5, -5 and -5. There are two positive numbers here and four negative numbers; the positive difference between the two types of numbers is 2.
Case 2: The six numbers could be -5, -5, 10, 0, 0 and 0. There is one positive number and two negative numbers; the positive difference between the two types of numbers is 1.
These are two different answers to the question asked.
The combination of statements is insufficient, answer option C can be eliminated.
The correct answer option is E.
The average of a list of six numbers is equal to zero. Therefore, the sum of these numbers is zero. It is important to consider different cases that ensure that the sum of the numbers is zero.
We need to find the positive difference between two numbers – the number of positive numbers in the list and the number of negative numbers in the list.
The term positive difference may hint that the two numbers are distinct and not the same.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: Each of the positive numbers in the list equals 10.
Case 1: The six numbers could be 10, 10, -10, -5, -5 and 0. There are two positive numbers here and three negative numbers; the positive difference between the two types of numbers is 1.
Case 2: The six numbers could be 10, -2, -2, -2, -2, and -2. There is one positive number and five negative numbers; the positive difference between the two types of numbers is 4.
These are two different answers to the question asked.
Statement 1 is insufficient, answer options A and D can be eliminated.
Statement 2: Each of the negative numbers in the list equals −5.
Case 1: The six numbers could be -5, 1, 1, 1, 1 and 1. There are five positive numbers here and one negative number; the positive difference between the two types of numbers is 4.
Case 2: The six numbers could be -5, -5, 10, 0, 0 and 0. There is one positive number and two negative numbers; the positive difference between the two types of numbers is 1.
These are two different answers to the question asked.
Statement 2 is insufficient, answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: Each of the positive numbers in the list equals 10.
From statement 2: Each of the negative numbers in the list equals -5.
Case 1: The six numbers could be 10, 10, -5, -5, -5 and -5. There are two positive numbers here and four negative numbers; the positive difference between the two types of numbers is 2.
Case 2: The six numbers could be -5, -5, 10, 0, 0 and 0. There is one positive number and two negative numbers; the positive difference between the two types of numbers is 1.
These are two different answers to the question asked.
The combination of statements is insufficient, answer option C can be eliminated.
The correct answer option is E.
17 Dec 2025, 17:53
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